1. Field of the Invention
The present invention relates to a pattern identification apparatus and a method thereof, an abnormal pattern detection apparatus and a method thereof, and a program. Particularly, the present invention relates to a pattern identification technique and an abnormal pattern detection technique, which are robust against various kinds of variations, in a pattern to be identified, caused by a difference in a data acquisition environment or noise added upon data acquisition.
2. Description of the Related Art
A so-called pattern identification technique of identifying one of a plurality of predefined classes to which input data belongs is known. Various methods have been proposed as pattern identification techniques robust against various kinds of input pattern variations caused by, for example, a difference in a data acquisition environment or noise added upon data acquisition.
A subspace method is disclosed in S. Watanabe and N. Pakvasa, “Subspace Method of Pattern Recognition”, Proceedings of 1st International Joint Conference of Pattern Recognition, pp. 25-32, 1973 (Watanabe-Pakvasa). A kernel nonlinear subspace method that has improved the above subspace method is disclosed in Eisaku Maeda and Hiroshi Murase, “Pattern Recognition by Kernel Nonlinear Subspace Method”, IEICE Transactions D-II, Vol. J82-D-II No. 4, pp. 600-612, April 1999 (Maeda-Murase hereinafter). A kernel nonlinear mutual subspace method is disclosed in Hitoshi Sakano, Naoki Takegawa, and Taichi Nakamura, “Object Recognition by Kernel Nonlinear Mutual Subspace Method”, IEICE Transactions D-II, Vol. J84-D-II No. 8, pp. 1549-1556, August 2001 (Sakano-Takegawa-Nakamura hereinafter). In these methods, first, subspaces including the data sets of the respective classes are obtained using principal component analysis or kernel nonlinear principal component analysis described in Bernhard Scholkopf, Alexander Smola, and Klaus-Robert Muller, “Nonlinear Component Analysis as a Kernel Eigenvalue Problem”, Neural Computation, Vol. 10, pp. 1299-1319, 1998 (Scholkopf-Smola-Muller hereinafter). The subspaces are compared with input data or a subspace obtained from input data, thereby identifying which class includes the input pattern.
In a method disclosed in Jorma Laaksonen, “Local Subspace Classifier”, Proceedings of 7th International Conference on Artificial Neural Networks, pp. 637-642, 1997, (Laaksonen hereinafter), first, the linear subspaces of the respective classes are formed using, of the data of the respective classes, only neighboring data of input identification target data. The projection distance of the input identification target data to each subspace is obtained. The projection distances of the classes are compared, thereby identifying which class includes the identification target data. Such a method using only neighboring local data can reduce the adverse effect generated by the nonlinear data distribution.
On the other hand, nonlinear dimension compression methods have been proposed recently, which are represented by Isomap disclosed in Joshua B. Tenenbaum, Vin de Silva, and John C. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction”, Science, Vol. 290, pp. 2319-2323, 2000 (Tenenbaum-Silva-Langford hereinafter) and LLE (Locally Linear Embedding) disclosed in Sam T. Roweis and Lawrence K. Saul, “Nonlinear Dimensionality Reduction by Locally Linear Embedding”, Science, Vol. 290, pp. 2323-2326, 2000 (Roweis-Saul hereinafter). These prior art works provide a method of mapping data, which is supposed to exist on a lower-dimensional hypersurface generally called a manifold in a high-dimensional space, onto a new low-dimensional space which maintains the surface shape unique to the manifold to an acceptable level.
The above-described methods are successful in efficient pattern expression in the sense that they can express data in a lower-dimensional space. However, their methods are not always optimal because they do not use information representing which class includes data.
Japanese Patent Laid-Open No. 2005-535017 discloses an arrangement for expressing an image for pattern classification by extending the conventional Isomap method using a kernel Fisher linear discriminant function or Fisher linear discriminant function. Bisser Raytchev, Ikushi Yoda, and Katsuhiko Sakaue, “Multi-View Face Recognition By Nonlinear Dimensionality Reduction and Generalized Linear Models”, Proceedings of 7th International Conference on Automatic Face Gesture Recognition, pp. 625-630, 2006, (Raytchev-Yoda-Sakaue hereinafter) discloses, as an improvement of the conventional Isomap method, a method of forming a mapping which increases the degree of separation between classes by forcibly increasing the geodesic distance between data belonging to different classes.
In the above-described conventional arrangements, however, it is difficult to identify a pattern which cannot undergo simple modeling because it has a complex distribution in the original feature space in accordance with various variations in input data, including variations in the illumination condition and the position and direction of a pattern recognition target. This has produced a demand for increasing the robustness against various variations in input data.
This will be described briefly. Assume that a gray-scale image of an extracted human face including, for example, 20×20 pixels is input to identify the person to whom the face image belongs. In this case, the 20×20 pixel gray-scale image can be regarded as a 20×20=400-dimensional vector with pixel values being arranged as elements by raster scan. At this time, one pattern corresponds to one point in the 400-dimensional space. Generally, a set of patterns for a specific class, for example, “face of Mr. A” forms a hypersurface generally called a manifold which has a smaller number of dimensions as compared to the 400-dimensional space. That is, 400 dimensions are redundant for expressing “face of Mr. A”, and a lower-dimensional space suffices.
The Watanabe-Pakvasa's subspace method executes pattern identification to determine which class includes input data using such a characteristic that a lower-dimensional space can express the data set of a certain class. In the subspace method, PCA (Principal Component Analysis) is applied to each of the data sets of the respective classes, thereby obtaining in advance a lower-dimensional subspace that expresses the data set of each class. A pattern is identified using the manner in which the input data is expressed in the subspace. More specifically, the projection lengths or projection distances of the input data to the subspaces are compared, thereby identifying the class which includes (or does not include) the input data. However, the PCA which assumes a normal pattern distribution cannot always obtain a sufficient low-dimensional expression for a set of patterns essentially including nonlinear variations such as a variation in the face direction.
The Maeda-Murase kernel nonlinear subspace method can even cope with a data set having a nonlinear distribution by replacing the PCA in the subspace method with the Scholkopf-Smola-Muller kernel nonlinear principal component analysis. The kernel nonlinear principal component analysis is generally called KPCA (Kernel PCA). However, even KPCA cannot always obtain a low-dimensional expression that approximates a manifold structure formed by the data set of a certain class.
The arrangements described in the remaining references are also required to further improve the robustness against various variations in input data.